Improving the quality of the content is likely to have a far greater positive effect than changing the domain name.
Unless the domain name is something that might be confusing or off-putting to potential customers, I wouldn't worry too much about it.
I have friends who were advised to do this, and it made not a shred of difference to their ranking. More recently, I had problems with a domain owned by somebody else which they had redirected to one of my clients' sites. Google started showing our home page with the URL of the redirected domain, not the correct domain. All images on that pages also showed up in Google searches under the redirected domain. Even more worryingly, the other 21 pages of our site suddenly ceased to be indexed by Google at all. (AFAIK, there were no problems with any other search engine, only Google.) For that reason alone, I would never try to use a domain redirect in this way.